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Paraconsistent query answering systems
 International Conference on Flexible Query Answering Systems
, 2002
"... Abstract. Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of par ..."
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Abstract. Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in query answering systems. We compare the paraconsistent and the nonmonotonic solutions to the problem of contradictions. We propose a manyvalued paraconsistent logic based on a simple notion of indeterminacy. In particular we describe the semantics of the logic using key equalities for the logical operators. We relate our approach to works on bilattices. We also discuss and provide formalizations of two case studies, notably the wellknown example involving penguins and a more interesting example in the domain of medicine. Paraconsistent logic can be seen as an alternative, for example, to nonmonotonic logic. Nonmonotonists reject monotony because they think that there are experiences (most of the time involving birds) which show that monotony is wrong and in particular leads to some contradictions. But one who thinks the paraconsistent way would reject the principle of non contradiction and not monotony. The strategy of the paraconsistentist is more imaginative, he accepts to see penguins flying in the sky of Hawai’s beaches and pink floyds surfing on Antarctica’s permafrost. It seems to us that the future shall give the preference to paraconsistent logic taking in account the progress of genitical biology which already produces chicken without feathers, and in the future we may have flying pigs. In such an absurd world, it will make no sense to reason by default, because everything could be true by default.
A paraconsistent higher order logic
 INTERNATIONAL WORKSHOP ON PARACONSISTENT COMPUTATIONAL LOGIC, VOLUME 95 OF ROSKILDE UNIVERSITY, COMPUTER SCIENCE, TECHNICAL REPORTS
, 2004
"... Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paracons ..."
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Cited by 6 (6 self)
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Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledgebased systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional manyvalued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.
A Query Construct for Paraconsistent Databases
 In Proceedings of the 7th International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems
, 1998
"... A data model has recently been developed for representing and manipulating two kinds of uncertain information in databases: incomplete and inconsistent. The model is based on 4valued relations, called paraconsistent relations, and has already been employed for developing elegant methods for model c ..."
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A data model has recently been developed for representing and manipulating two kinds of uncertain information in databases: incomplete and inconsistent. The model is based on 4valued relations, called paraconsistent relations, and has already been employed for developing elegant methods for model computation of general deductive databases. Here, we present an SQLlike SELECT statement construct for posing queries to paraconsistent databases based on this model. The syntax of our generalised SELECT statement is similar to that of the usual SELECT statement of SQL, but its semantics is based on a 4valued logic, making it an effective tool for querying paraconsistent databases. 1 Introduction One of the causes of uncertainty in information systems is the adoption of sensors on the realworld for the purpose of determining the truthvalue of a proposition. In many situations, such sensors are the only available method for this task. Moreover, as the reliability of most sensors falls short...
INTERVAL NEUTROSOPHIC SETS AND LOGIC: THEORY AND APPLICATIONS IN COMPUTING
, 2006
"... A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to ..."
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Cited by 6 (2 self)
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A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the settheoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the settheoretic operators and relationtheoretic operators of fuzzy relations and paraconsistent relationsto neutrosophic relations. We propose the generalized SQL query constructs and tuplerelational calculus for Neutrosophic Data Model.
Computing The WellFounded Model Of Deductive Databases
 The International Journal of Uncertainty, Fuzziness and Knowledgebased Systems
, 1996
"... this paper, we show how paraconsistent relations can be used to capture a partial model of a general deductive database and how the associated algebra can be used to compute the wellfounded model of the database. The central idea in arriving at this model is to associate paraconsistent relations wi ..."
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Cited by 5 (2 self)
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this paper, we show how paraconsistent relations can be used to capture a partial model of a general deductive database and how the associated algebra can be used to compute the wellfounded model of the database. The central idea in arriving at this model is to associate paraconsistent relations with the predicate symbols of the given general deductive database. Our method for constructing the wellfounded model involves two steps. In the first step, the database clauses are converted into paraconsistent relation definitions involving the operators on them. In the second step, these definitions are used to iteratively construct the model. Computing the Wellfounded Model of Deductive Databases 3 The approach presented in this paper lays an algebraic foundation for query processing and optimization for general deductive databases. Query processing will proceed in a bottomup manner and will use popular rewriting strategies, such as Magic Sets [15], to focus the search for answers. Query optimization can also be achieved at the level of the paraconsistent relational algebra by making use of the laws of equalities. The rest of this paper is organized as follows. Section 2 provides a brief overview of the wellfounded model. Section 3 gives a quick introduction to paraconsistent relations and some algebraic operators over them. Section 4 presents the first part of the model construction method, namely an algorithm to convert the database clauses into algebraic equations defining paraconsistent relations. Section 5 presents the second part of the method, namely an algorithm to incrementally construct the paraconsistent relations using the equations constructed earlier. Finally, Section 6 contains some concluding remarks and comparisons with related work.
Paraconsistent knowledge bases and manyvalued logic
 International Baltic Conference on Databases and Information Systems, Volume
, 2002
"... Abstract Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of p ..."
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Abstract Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge bases. We present a paraconsistent manyvalued logic with a simple and new semantics for the logical operators. In particular we compare our approach with work based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. 1.
Paraconsistent assertions
 In Second German Conference on Multiagent System Technologies
, 2004
"... Abstract. Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion. We argue that paraconsistent logics are especially advantageous in order to deal with assertions made ..."
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Abstract. Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion. We argue that paraconsistent logics are especially advantageous in order to deal with assertions made by intelligent agents. Other propositional attitudes like knowledge and beliefs can in principle be treated along the same lines. We propose a manyvalued paraconsistent logic based on a simple notion of indeterminacy. The proposed paraconsistent logic has a semantics that extends the one of classical logic and it is described using key equalities for the logical operators. A case study is included. We briefly compare with logics based on bilattices. We finally investigate how to translate the paraconsistent logic into classical predicate logic thereby allowing us to make use of automated deduction of classical logic in the future. We base our initial translation on recent work by Muskens. Our final translation is polynomial in the size of the translated formula and follows the semantics for the paraconsistent logic directly. The major motivation behind paraconsistent logic has always been the thought that in certain circumstances we may be in a situation where our information or theory is inconsistent, and yet where we are required to draw inferences in a sensible fashion... Numerous examples of inconsistent information/theories from which one might want to draw inferences in a controlled way have been offered by paraconsistent logicians. For example: 1. information in a computer data base; 2. various scientific theories; 3. constitutions and other legal documents; 4. descriptions of fictional (and other nonexistent) objects; 5. descriptions of counterfactual situations. The first of these is fairly obvious...
A Temporal Paraconsistent Relational Algebra for Incomplete and Inconsistent Information
 In Proceedings of the 33rd ACM Southeast Conference
, 1995
"... We construct a framework for natural handling of incomplete and inconsistent information in temporal databases. Central to this framework are structures that we call timevarying paraconsistent relations, which are essentially 4valued relations that vary over time. For such structures, we present a ..."
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We construct a framework for natural handling of incomplete and inconsistent information in temporal databases. Central to this framework are structures that we call timevarying paraconsistent relations, which are essentially 4valued relations that vary over time. For such structures, we present an algebra based on temporal semantics in which there is no explicit manipulation of time indices, yet it is rich enough to express recursive equations as queries. The algebra is a consistent extension of the relational algebra; it supports basic algebraic equivalences, and has a welldefined formal semantics. We also provide many examples of queries expressed in this algebra. To our knowledge, our framework is the first treatment of inconsistent information in the context of temporal databases. 1 Introduction One limitation of the relational data model of Codd [7] is its lack of applicability to nonclassical situations. These are situations involving incompleteness, or more importantly, eve...
A data model based on paraconsistent intuitionistic fuzzy relations
 Proceedings of 15 th International Symposium on Methodology for Intelligent System
, 2005
"... Abstract. Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or intervalvalued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truthmembership and f is grade of falsemembership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ..."
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Abstract. Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or intervalvalued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truthmembership and f is grade of falsemembership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ≤ t + f ≤ 2. In this paper, we present a generalization of the relational model of data based on paraconsistent intuitionistic fuzzy set. Our data model is capable of manipulating incomplete as well as inconsistent information. Associated with each relation there are two membership functions which keep track of the extent to which we believe the tuple is in the relation and the extent to which we believe that it is not in the relation. In order to handle inconsistent situations, we propose an operator, called “split”, to transform inconsistent paraconsistent intuitionistic fuzzy relations into pseudoconsistent paraconsistent intuitionistic fuzzy relations. We may then manipulate these pseudoconsistent paraconsistent intuitionistic fuzzy relations by performing settheoretic and relationtheoretic operations on them. Finally, we can use another operator, called “combine”, to transform the results back to paraconsistent intuitionistic fuzzy relations. For this model, we define algebraic operators that are generalization of the usual operators such as union, selection, join on fuzzy relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. 1
Under the Direction of Rajshekhar Sunderraman
"... A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to ..."
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A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the settheoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the settheoretic operators and relationtheoretic operators of fuzzy relations and paraconsistent relations to neutrosophic relations. We propose the generalized SQL query constructs and tuplerelational calculus for Neutrosophic Data Model.